CHARACTERIZATION OF POWDERS AND POROUS MATERIALS

Outline Theory of Adsorption Surface area and porosity Micro-Porosity

Characterization of Powders and Porous Materials with Pharmaceutical Excipinent Case Studies Jeffrey Kenvin, PhD Micromeritics Instrument Corporation

July 2008

[email protected]

Surface area and porosity


Outline

1

Theory of Adsorption

2

Surface area and porosity Surface Area Thickness Porosity Macro-porosity

3

Micro-Porosity

[email protected]



Adsorption

Definitions Adsorption Adsorbate Adsorptive Adsorbent

→ → → →

Enrichment in an interfacial layer Substance in the adsorbed state Adsorbable substance in the fluid phase Solid material on which adsorption occurs

[email protected]



Definitions cont’d

Preparation Clean the surface Remove volatiles 1 2 3

Water CO2 Solvents

Controlled environment 1 2

Inert purge or vacuum Temperature control

Avoid Phase Changes

[email protected]



Definitions cont’d

Physical Adsorption Physisorption p sat or Psat p ◦ or P◦

→ → →

Adsorption without chemical bonding Saturation pressure (of the cryogen) Saturation pressure of the adsorptive

Chemical Adsorption Chemisorption

→

Adsorption involving chemical bonding

[email protected]



Adsorption Physical Adsorption General phenomenon with a relatively low degree of specificity. Retains identity; desorbs to fluid phase in its original form. Exothermic adsorption similar to the energy of condensation. Rapid equilibration; transport limited. Chemical Adsorption Dependent on reactivity of adsorbent and adsorptive. Chemisorbed molecule may react or dissociate. Energy is similar to energy change for chemical reaction. Activated process at elevated temperature. [email protected]



Adsorption Physical Adsorption Molecules from the gas phase strike the surface. At equilibrium the molecule adsorbs, lose the heat of adsorption (q), and subsequently desorb from surface. At equilibrium the rate of condensation = the rate of desorption Constant surface coverage at equilibrium.

[email protected]



Adsorption Physical Adsorption Surface features change the adsorption potential. Surface area models neglect the effects of localized phenomenon. Curve surfaces or roughness provide enhanced adsorption potential.

[email protected]



Multi-Layer Physical Adsorption As the system pressure is increased (gas concentration also increases) multiple layers sorb to the surface. The monolayer coverage, a densely packed single adsorbed layer is used for determining surface area. As pressure is further increased and adsorption proceeds gas condenses in the pores and this volume of condensed adsorptive is used for characterizing porosity. [email protected]



Adsorption Surface area is easily estimated if the number of N2 molecules that form monolayer is known. Calculating Surface Area Surface Area = nm ×

Na Vm Na × σA = × × σA w Vg w

where: nm Vm Vg Na w σA

= = = = = =

Monolayer quantity, mol Monolayer volume, cm3 Molar volume of gas at STP, 22414 cm3 /mol Avogadro’s number, 6.023×1023 molecules/mol sample mass, g Cross-sectional area of the adsorbate, m2 [email protected]



Physisorption - Hardware

Key Features Stainless steel manifold

Dedicated vacuum system

1000, 10, 1 torr transducers

Cryogen level control/long dewar life

[email protected]



Physisorption - Special Considerations Saturation pressure and temperature for N2 or Ar “Measured” value of p ◦ Calculate bath temperature from measured p ◦ Saturation pressure and temperature for Kr “Measured” value of p sat of N2 sat Calculate bath temperature from pN 2

Calculate p ◦ from calculated temperature Saturation pressure and temperature for CO2 “Entered” value of bath temperature Calculate p ◦ from entered temperature [email protected]



Adsorptive Properties Gas specific Non-ideality Excess N2 at 77 K All gas accounting calculations

Density conversion factor Convert from measured volume to a liquid volume t-plot, BJH, pore volume calculations

Cross-sectional area Size of a nitrogen molecule BET, Langmuir, BJH, HK

Hard sphere diameter pressure correction for micro pore analyses

[email protected]



Non-ideality Accurately account for the Real gas behavior V measured 6.1103 ◦ p◦ = 0.957 z p ,T = = 6.3842 V ideal The ideal gas law only accounts for 95.7% of the nitrogen; there is a 4.3% excess α=

1 z

1 −1 0.957 − 1 = = 0.0000594 mmHg−1 p◦ 755.09

The non-ideality factor gives us the excess nitrogen per unit of pressure

[email protected]



Density conversion factor

Convert quantity adsorbed to a pore volume φ=

Vliquid ρgas 0.0347 = = = 0.00155 ρliquid 22.414l/mol 22414

http://webbook.nist.gov/chemistry/fluid/

[email protected]



Adsorption

Isotherms Quantity adsorbed vs. pressure. Pressure is usually varied from vacuum to near atmospheric. Constant temperature. Quantity adsorbed is normalized for adsorbent mass. Six isotherm classifications

Types I, II, and IV - most materials Type III - uncommon Type V - rare Type IV - highly uniform surface

[email protected]



nads

Isotherm classifications

I

II

III

IV

V

VI

P

[email protected]



Isotherm classifications - rearrangement

nads

I

II

III

IV

V

P [email protected]


VI


nads

Isotherm classifications - similarity

I

II

III

VI

IV

V

P

[email protected]



Surface Area Thickness Porosity Macro-porosity

Type I - Isotherm

I

Micropore filling

nads

Langmuir Isotherm Mono-layer adsorption Finely divided surface Limiting amount adsorbed as p/p◦ approaches 1 P

[email protected]




Type I Isotherms - Y & X Zeolite Faujasite 250

Y Zeolite X Zeolite

Quantity Adsorbed, cm3/g

200

150

100

50

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type I Isotherms - Y & X Zeolite Faujasite 250

Y Zeolite X Zeolite


200

150

100

50

0 1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - Fluid Cracking Catalyst Fluid Cracking Catalyst, 0.8nm pores 100

Adsorption Desorption

90 Quantity Adsorbed, cm3/g

80 70 60 50 40 30 20 10 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type I Isotherms - Fluid Cracking Catalyst Fluid Cracking Catalyst, 0.8nm pores 100


90 Quantity Adsorbed, cm3/g

80 70 60 50 40 30 20 10 0 1e-07

1e-06

1e-05

1e-04

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - Y Zeolite & FCC 0.8nm pores 250

Y Zeolite FCC


200

150

100

50

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type I Isotherms - Y Zeolite & FCC 0.8nm pores 250

Y Zeolite FCC


200

150

100

50

0 1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - ZSM-5 ZSM-5, 0.5-0.6nm pores 160

Adsorption


140 120 100 80 60 40 20 0 0

0.1

0.2

0.3

0.4

0.5

0.6

p/po

[email protected]


0.7

0.8



Type I Isotherms - ZSM-5 ZSM-5, 0.5-0.6nm pores 160

Adsorption


140 120 100 80 60 40 20 0 1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - TS-1 Titano-silicate, 0.5nm pores 180

Adsorption


160 140 120 100 80 60 40 20 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type I Isotherms - TS-1 Titano-silicate, 0.5nm pores 180

Adsorption


160 140 120 100 80 60 40 20 0 1e-07

1e-06

1e-05

1e-04

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - TS-1 & ZSM-5 0.5nm pores 180

TS-1 ZSM-5


160 140 120 100 80 60 40 20 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type I Isotherms - TS-1 & ZSM-5 0.5nm pores 180


160

TS-1 ZSM-5

140 120 100 80 60 40 20 0 1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Type I Isotherms - Single Wall Carbon Nanotubes Carbon Nanotubes 300

Adsorption


250

200

150

100

50

0 0

0.05

0.1

0.15

0.2

0.25

p/po

[email protected]


0.3

0.35



Type I Isotherms - Single Wall Carbon Nanotubes Carbon Nanotubes 300


250

200

150

100

50

0 1e-08

1e-07

1e-06

1e-05

1e-04

0.001

0.01

p/po

[email protected]


0.1

1



Langmuir Langmuir Model of Type I Isotherm dN a −E = ap(1 − θ) − βθ exp = 0, equilibrium dt RT −E ap(1 − θ) = βθ exp RT b = K exp(E /RT ) where:

θ a β p K

≡ ≡ ≡ ≡ ≡

fraction of surface occupied adsorption coefficient desorption coefficient equilibrium pressure a/β

[email protected]




Langmuir

Langmuir Model θ = bp 1−θ θ → 0, Langmuir model → Henry’s law θ lim =θ θ→0 1 − θ θ = bp

[email protected]




Langmuir

Langmuir Model of Type I Isotherm n =θ nm rearrange the Langmuir model to a more convenient form . . . n bp = nm 1 + bp where:

n nm

≡ ≡

[email protected]

quantity adsorbed monolayer capacity




N2 Adsorption on 13x Zeolite Nitrogen Adsorption, 13x Zeolite Adsorption

Silica-alumina Ca+ exchanged zeolite

3

Type I Crystalline 10 (8) ˚ A, pore

Quantity Adsorbed, cm /g STP

140 120 100 80 60 40 20 0

0

[email protected]

0.2

0.4 0.6 Pressure, mmHg


0.8

1



N2 Adsorption on 13x Zeolite Langmuir Transformation, 13x Zeolite 13X

0.007

p/Q, mmHg/(cm3/g STP)

0.006 0.005 0.004 0.003 0.002 0.001 0

0

0.2


0.8

1

Linearized Langmuir Model → 620m2 /g , b = 563.5/mmHg p 1 p = + n bnm nm [email protected]




N2 Adsorption on 13x Zeolite 13x Zeolite

Quantity Adsorbed, cm3/g STP

140 120 100 80 60 40 20 0

13X Langmuir model 0

0.2


[email protected]

0.8


1



Type II - Isotherm

II

Uniform surface

nads

BET Isotherm Non-porous surface Multilayer adsorption Infinite adsorption as p/p◦ approaches 1 P

[email protected]




Type II Isotherms - Silica 1000˚ A Silica, 100nm pores 40



35 30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type II Isotherms - Silica 1000˚ A Silica, 100nm pores 40


35 30 25 20 15 10 5 0 1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Type II Isotherms - SRB D5 Carbon Black SRB D5 Carbon Black 60

Adsorption


50

40

30

20

10

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

p/po

[email protected]


0.8

0.9

1



Type II Isotherms - SRB D5 Carbon Black SRB D5 Carbon Black 60


50

40

30

20

10

0 1e-07

1e-06

1e-05

0.0001

0.001

0.01

p/po

[email protected]


0.1

1



Brunauer, Emmett, and Teller

Surface Area Stephen Brunauer Paul Emmett Edward Teller N2 adsorption Fixed Nitrogen Laboratory,1938 Second most cited reference over a 50 year period

[email protected]




BET Assumptions

Surface Area Multi-layer adsorption Non-porous, Uniform surface Heat of adsorption for the first layer is higher than successive layers. Heat of adsorption for second and successive layers equals the heat of liquefaction Lateral interactions of adsorbed molecules are ignored

[email protected]




BET Model First Layer a1 pθ0 = b1 θ1 exp where: b1 θ1 exp

a1 pθ0 −E1 RT

θ0 θ1

−E1 RT

≡

rate of condensation

≡

rate of evaporation

≡ ≡

fraction of bare surface fraction of covered surface

Rate of condensation = rate of desorption b1 −E1 pθ0 = θ1 exp a1 RT [email protected]




BET Model Ei>1 = El

All Layers

−E1 RT

bi /ai = g

−E1 RT

b1 −E1 pθ0 = θ1 exp a1 RT b2 −E2 b2 −El −El pθ1 = θ2 exp pθ1 = θ2 exp pθ1 = g θ2 exp a2 RT a2 RT RT −E3 b3 −El b3 −El pθ2 = θ3 exp pθ2 = θ3 exp pθ2 = g θ3 exp a3 RT a3 RT RT

b1 pθ0 = θ1 exp a1

b1 pθ0 = θ1 exp a1

.. . pθi−1

bi = θi exp ai

.. .

−Ei RT

pθi−1

.. .

bi = θi exp ai

[email protected]

−El RT

pθi−1 = g θi exp


−El RT



BET Model

Sum of Surface Fractions θ0 + θ1 + θ 2 + θ3 + . . . + θ i + · · · = 1 Total Quantity Adsorbed n = nm (1θ1 + 2θ2 + 3θ3 + . . . + iθi + · · · ) Multilayer has Infinite Thickness p = 1, i → inf p◦

[email protected]





Type II Isotherm n Cx = nm (1 − x)(1 − x + Cx) where:

n nm C x

≡ ≡ ≡ ≡

quantity adsorbed monolayer capacity −El adsorption coefficient, ≈ exp E1RT relative pressure at equilibrium, p/p◦

[email protected]





Linearized BET p 1 C −1 p = + × ◦ − p) nm C nm C p

n(p ◦ 1 2 3 4

p p n(p ◦ −p) vs. p ◦ , 1 nm = slope+intercept slope C = 1 + intercept

Plot

0.05 ≤

p p◦

≤ 0.30

C >0

[email protected]




N2 Adsorption on Macro-Porous Silica Nitrogen Isotherm, Lichrosphere 1000 40


Type II Amorphous ˚, pore 1000A Desorption Lack of Hysteresis


35 30 25 20 15 10 5 0

0

0.2

0.4

0.6

Relative Pressure, p/po

[email protected]


0.8

1



N2 - BET Transformation - 25.7 m2 /g Linear BET, Lichrosphere 1000 0.045

Lic 1000

0.04 0.035

0.025

o

1/Q(p /p-1)

0.03

0.02 0.015 0.01 0.005 0

0

0.05

0.1

0.15

0.2

0.25


[email protected]


0.3



N2 Adsorption on Carbon Black SRB D5 Carbon Black 60

Adsorption

Type II Amorphous Nano-particle


50

40

30

20

10

0 0

0.1

0.2

0.3

0.4

0.5 p/po

[email protected]


0.6

0.7

0.8

0.9

1



SRB D5 Carbon Black - 21.2 m2 /g SRB D5 0.07 0.06

1/(qads(po/p - 1))

0.05 0.04 0.03 0.02 0.01 0 0

0.05

0.1

0.15

0.2

0.25

p/po

[email protected]


0.3



Special considerations Low Surface Area Materials Krypton - p ◦ is 1/300 of N2 p ◦ Eliminate “void space errors” Approximately same quantity adsorbed for Kr or N2 Same error for “void space” Error is proportional to pe Vfs Typical N2 experiment 35 - 220 mmHg Typical Kr experiment 0.01 - 0.5 mmHg Additonal Hardware Turbo-pump 10 torr transducer [email protected]




Alternate approach to Kr

Balanced Tube Design Balance tube eliminates “void space” errors Rapid analysis

[email protected]




Special Case - Single Point Surface Area Linearized BET Transformation 1 C −1 p p = + × ◦ − p) nm C nm C p

n(p ◦

Assume C → ∞ (C > 100)

1 nm C

C −1 nm C

lim

C →∞

lim

C →∞

=0 =

1 nm

Single point estimate of nm p nm = n 1 − ◦ p [email protected]




Physisorption - Dynamic Adsorption Hardware

Key Features Rapid Analysis

High-sensitivity

Wide range of materials

Low cost

[email protected]




Physisorption - Dynamic Adsorption Dynamic N2 Adsorption/Desorption, SiO2-Al2O3 1.5

Analysis Tips

2

1

Desorption peak is used for Vm Simple calibration N2 injections

3

Not limited to N2 adsorption

TCD Signal, V

1

0.5

N2 Adsorption

0 N2 Desorption

-0.5

-1

Kr , Ar , CO2 , . . . -1.5 0

[email protected]

1

2

3

4 5 time, minutes


6

7

8

9



Physisorption - Special Case - Magnesium Stearate Static N2 Adsorption, Magnesium Stearate 35


30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


[email protected]


0.9

1



Physisorption - BET Surface Area Magnesium Stearate Static N2 Adsorption, Magnesium Stearate 0.22 0.2 0.18

o

p/(Q*(p -p))

0.16 9.3 m2/g

0.14 0.12 0.1 7.14 m2/g

0.08 0.06 0.04 0

0.05

0.1

0.15

0.2

0.25


[email protected]


0.3



Excipients Pharmaceutical excipients Substances other than the pharmacologically active drug or prodrug which are included in the manufacturing process or are contained in a finished pharmaceutical product dosage form. Commonly used excipients Calcium stearate Gelatin

Sodium stearate Stearic acid

Lactose Magnesium stearate Microcrystalline cellulose Silicon dioxide [email protected]

Sucrose Talc Titanium dioxide Surface area and porosity



Investigate the impact of preparation temperature

Both excipients and APIs may be sensitive to temperature. The preparation (removal of moisture, solvents, and ambient gases) is often performed at or near room temperature. 1 2 3

Purge with inert gas (nitrogen) or evacuate Control temperature at 40◦ C Duration 4 - 24 hours

[email protected]




Oxides

Commonly used oxides 1

2

3

Aluminum oxide Alumina - Al2 O3

Not chemically active

Silicon dioxide Silica - SiO2

Do not dissolve

Titanium dioxide Titania - TiO2

Range of surface area and porosity

[email protected]

Stable Range of particle sizes




Effect of preparation temperature on the SSA of Al2 O3 α-alumina 0.44

0.4

2

Surface Area, m /g

0.42

0.38 0.36 0.34 0.32 0.3 20

40

60 80 Preparation Temperature, °C

100

120

Surface area increases 33% as preparation temperature is increased from 40 to 100◦ C as CO2 is removed. [email protected]




Effect of preparation temperature on the SSA of SiO2 Silicon Dioxide 376 375

2

Surface Area, m /g

374 373 372 371 370 369 368 367 20

40


100

120

Surface area increases 3% as preparation temperature is increased from 40 to 60◦ C as H2 O is removed. [email protected]




Effect of preparation temperature on the SSA of TiO2 Titanium Dioxide 9.3

9.2

2

Surface Area, m /g

9.25

9.15 9.1 9.05 9 8.95 50

100 150 200 Preparation Temperature, °C

250

A slight increase in SSA is observed for the titania. [email protected]


300



Glidants and Lubricants

for making tablets 1

Stearic Acid

2

Calcium Stearate

3

Magnesium Stearate

4

Sodium Stearate

5

Talc

[email protected]




Effect of temperature on the SSA of Stearic Acid Stearic Acid 0.9 0.85 0.8

2

Surface Area, m /g

0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 20

40


100

120

The loss is surface area indicates the melting of the stearic acid small particles → large particles. [email protected]




Effect of temperature on the SSA of Ca2+ Stearate Calcium Stearate 7

6.6

2

Surface Area, m /g

6.8

6.4 6.2 6 5.8 5.6 20

40


100

SSA drops as temperature increases. [email protected]


120



Effect of temperature on the SSA of Mg2+ Stearate Magnesium Stearate 3.2

3

2

Surface Area, m /g

3.1

2.9 2.8 2.7 2.6 2.5 20

40


100

SSA decreases 20% as temperature increases. [email protected]


120



Effect of temperature on the SSA of Na+ Stearate Sodium Stearate 7.7

7.6

2

Surface Area, m /g

7.65

7.55 7.5 7.45 7.4 7.35 20

40


100

120

SSA reaches at optimum at 60◦ C and then decreases with increasing temperature. [email protected]




Effect of temperature on the SSA of Stearates Na+, Ca2+, Mg2+ Stearate, and Stearic Acid 8 7

Surface Area, m2/g

6 5 4 3 2 +

Na2+Stearate Ca 2+ Stearate Mg Stearate Stearic Acid

1 0 20

40


[email protected]

100


120



Effect of temperature on the SSA of Talc Talc 7.7

Surface Area, m2/g

7.65 7.6 7.55 7.5 7.45 7.4 7.35 20

40


[email protected]

100


120



Other Excipients

Binders and fillers 1 Gelatin - solution binder 2

Lactose - binder

3

Microcrystalline Cellulose - binder

4

Sucrose - filler

[email protected]




Effect of temperature on the SSA of Gelatin Gelatin 0.25 0.245

2

Surface Area, m /g

0.24 0.235 0.23 0.225 0.22 0.215 0.21 0.205 20

40


[email protected]

100


120



Effect of temperature on the SSA of Lactose Lactose Monohydrate 2.6 2.4

2

Surface Area, m /g

2.2 2 1.8 1.6 1.4 1.2 1 0.8 20

40


100

120

Significant increase in SSA as preparation temperature is increased. [email protected]




Effect of temperature on the SSA of Microcrystalline Cellulose Microcrystalline Cellulose 1.62

1.58

2

Surface Area, m /g

1.6

1.56 1.54 1.52 1.5 1.48 20

40


[email protected]

100


120



Effect of temperature on the SSA of Sucrose Sucrose 0.23

0.21

2

Surface Area, m /g

0.22

0.2 0.19 0.18 0.17 0.16 20

40


[email protected]

100


120



Type IV - Isotherm

IV

Reduced saturation pressure in pores Hysteresis

nads

Mesoporous Materials Multi-layer adsorption

Shape Tortuosity P

[email protected]




N2 Adsorption on Amorphous Silica-Alumina Amorphous Silica Alumina, 11nm pores 450


Type IV Amorphous ˚, pore 100A Desorption Hysteresis

Quantity adsorbed, cm3/g

400 350 300 250 200 150 100 50 0 0

0.1

0.2

0.3

0.4

0.5 p/po

[email protected]


0.6

0.7

0.8

0.9

1



N2 - BET Transformation - 215.5 m2 /g 0.007

2

BET Surface Area = 215.5 m /g 0.006

1/(qads(po/p - 1))

0.005 0.004 0.003 0.002 0.001 0 0

0.05

0.1

0.15

0.2

0.25

p/po

[email protected]


0.3

0.35



N2 Adsorption on MCM-41 Silica, 4 nm pores 600

Desorption Lack of Hysteresis

500 Quantity adsorbed, cm3/g

Type IV Mesoporous Silica A, 40˚ cylindrical pore


400

300

200

100

0 0

0.1

0.2

0.3

0.4

0.5 p/po

[email protected]


0.6

0.7

0.8

0.9

1



N2 - BET Transformation - 926.8 m2 /g 0.0016

BET Surface Area = 926.8

0.0014

1/(qads(po/p - 1))

0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0

0.05

0.1

0.15

0.2

0.25

p/po

[email protected]


0.3

0.35



Standard Isotherms

Thickness Monolayer region is sensitive to isotherm shape Multilayer region is not sensitive to isotherm shape Multilayer region is less dependent on the adsorbent structure Multilayer Thickness t = d0

n nm

where: d 0 ≡ thickness of the monolayer, d 0 = 3.54˚ A for N2

[email protected]




t-Plot → “Rules of Thumb” Plot Va vs. t Slope of a linear region corresponds to area Intercept from a linear region is a pore volume

nads

Based on BET surface area

thickness, Å [email protected]

thickness, Å Surface area and porosity



t-Plot → “Micro Porous Sample” Plot Va vs. t Slope corresponds to external (matrix) area Intercept is the micro pore volume t-curve is critical

nads

External Area

Flat Surface µ Pore Vol





t-Plot → “Meso Porous Sample” Plot Va vs. t Low ”t” slope is pore area Intercept is meso pore volume High ”t” slope is external area

nads

External Area

External Area

Meso Pore Vol Flat Surface

Flat Surface Pore Area

µ Pore Vol





Statistical t-Curve

Halsey t = 3.54 ×

−5 ln pp◦

!1 3

Harkins and Jura t=

13.99 0.034 − log10

[email protected]

!1 2

p p◦




Statistical t-Curve

Jaroniec et. al. t=

60.65 0.03071 − log10

!0.3968 p p◦

Broekhoff de Boer F (te ) = 2.303R

−16.11 + 0.1682e −0.1137te te2

[email protected]

, F (t) = R ln


p p◦



Statistical t-Curve

Exteranl Surface Area of Carbon Black Special application of t-plot to determine the external area of carbon. Replaces the traditional CTAB cetyltrimethyl ammonium bromide Carbon STSA t = 0.88

p p◦

2

+ 6.45

[email protected]

p p◦

+ 2.98




The t-Method t-Plot Statistical curves 20

Halsey Harkins and Jura Jaroniec et. al. Broekhoff de Boer

Thickness, angstroms

15

10

5

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

p/po

[email protected]


1



The t-Method t-Plot Silica surface with 1000 ˚ A pores DFT used to determine monolayer capacity 35


30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

o

p/p

[email protected]


1



The t-Method t-Plot Silica surface with 1000 ˚ A pores BET used to determine monolayer capacity 35

DFT BET


30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

o

p/p

[email protected]


1



The t-Method t-Plot Silica surface with 1000 ˚ A pores Silane treatment to remove OH −1 35

DFT ODMS


30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

p/po

[email protected]


1



The t-Method → Microporous sample - 13X t-Plot → external area = 201.3 m2 /g Faujasite - 13X Silica surface with 1000 ˚ A pores - DFT used for Vm 160 140


External area 120 100 80 60

Micropore filling

40 20 0 0

0.5

1 1.5 Thickness, angstroms

[email protected]

2


2.5



The t-Method → Microporous sample - Y Zeolite t-Plot → external area = 21.3 m2 /g Faujasite - Y Zeolite Silica reference curve 250

qads, cm3/g

200

150

100

50

0 0

2

4

6

[email protected]

8 10 thickness, Å

12

14


16



The t-Method → Microporous sample - FCC t-Plot → external area = 28.5 m2 /g FCC - Y Zeolite & binder Silica reference curve 80 70

qads, cm3/g

60 50 40 30 20 10 0 0

2

4

6

[email protected]

8 thickness, Å

10

12

14


16



The t-Method → Microporous sample - ZSM-5 t-Plot → external area = 116.7 m2 /g ZSM-5 Silica reference curve 160 140

qads, cm3/g

120 100 80 60 40 20 0 0

2

4

6

8

10

thickness, Å

[email protected]


12



The t-Method → Microporous sample - TS-1 t-Plot → external area = 119.9 m2 /g Titano-silicate Silica reference curve 200 180 160

qads, cm3/g

140 120 100 80 60 40 20 0 0

2

4

6

8

10

12

14

thickness, Å

[email protected]


16



The t-Method → Mesoporous sample - MCM 41 t-Plot → pore area = 699.4 m2 /g 40 ˚ A mesoporous silica, cylindrical pores ˚ pores - DFT used for Vm Silica surface with 1000 A 700


600 500 400 300 200

Pore area

100 0 0

2

4

6 8 Thickness, angstroms

[email protected]

10

12


14



The t-Method → Mesoporous sample - MCM 41 t-Plot → external area = 140.7 m2 /g 40 ˚ A mesoporous silica, cylindrical pores ˚ pores - DFT used for Vm Silica surface with 1000 A 600


500

External area

400

300

200

100

0 0

2

4


[email protected]

10

12


14



The t-Method → Mesoporous sample - Silicaalumina t-Plot → external area = 143 m2 /g 110 ˚ A mesoporous silica Silica surface with 1000 ˚ A pores - DFT used for Vm 400


350 300 250 200 150 100 50 0 0

2

4


[email protected]

10

12


14



The t-Method 600

40 angstrom 30 angstrom 110 angstrom 8 angstrom


500

400

300

200

100

0 0

2

4


[email protected]

10


12

14



The t-Method → SRB D5 - Carbon Black t-Plot → external area = 18.3 m2 /g D5 STSA for Carbon Black SRB D5 12

10

qads, cm3/g

8

6

4

2

0 0

1

2

3

[email protected]

4 5 thickness, Å

6

7


8

9



Excipients - t-plot Pharmaceutical excipients Use the t-plot method to determine if select excipients exhibit micro porosity or meso porosity Commonly used excipients Calcium stearate Gelatin

Sodium stearate Stearic acid

Lactose Magnesium stearate Microcrystalline cellulose Silicon dioxide [email protected]

Sucrose Talc Titanium dioxide




Effect of preparation temperature on the porosity of Calcium Stearate Calcium Stearate 5 4.5 4

Quantity, cm3/g

3.5 3 2.5 2 1.5 1 0.5 0 0

2

4

6

8

thickness, Å

[email protected]


10



Effect of preparation temperature on the porosity of Magnesium Stearate Magnesium Stearate 2.5

Quantity, cm3/g

2

1.5

1

0.5

0 0

2

4

6

8

thickness, Å

[email protected]


10



Effect of preparation temperature on the porosity of Microcrystalline cellulose Microcrystalline Cellulose 1.2

Quantity, cm3/g

1

0.8

0.6

0.4

0.2

0 0

2

4

6

8

thickness, Å

[email protected]


10



Effect of preparation temperature on the porosity of SiO2 Silicon Dioxide 250

Quantity, cm3/g

200

150

100

50

0 0

2

4

6

8

thickness, Å

[email protected]


10



Effect of preparation temperature on the porosity of Talc Talc 6

Quantity, cm3/g

5

4

3

2

1

0 0

2

4

6

8

thickness, Å

[email protected]


10



Effect of preparation temperature on the porosity of TiO2 Titanium Dioxide 5 4.5 4

Quantity, cm3/g

3.5 3 2.5 2 1.5 1 0.5 0 0

2

4

6

8

thickness, Å

[email protected]


10



Capillary Condensation

Mesoporous Adsorbed layer Condensed phase Liquid Nitrogen r t

[email protected]


r t



BJH Calculations

r r t

t

Pore Width Hydraulic radius Kelvin equation Adsorbed Layer Thickness equation or curve

[email protected]




BJH Calculations

Combine Kelvin Equation with the Thickness of the Adsorbed Layer rp = rk + t wp = 2 × (rk + t) where:

wp rp rk t

≡ ≡ ≡ ≡

pore width (diameter) pore radius hydraulic radius thickness of the adsorbed layer

[email protected]




BJH Calculations Kelvin Equation for Cylindrical Pores Calculate the hydraulic radius for capillary condensation in Meso-pores. Cylindrical geometry is the standard for BJH calculations. ˚, (reduced precision below 75 ˚ Pore size > 20 A A) RT ln where:

γ vl rk

p 2γv l = − p◦ rk

≡ ≡ ≡

[email protected]

surface tension liquid molar volume hydraulic radius




BJH Calculations

Kelvin Equation for Slit-shaped Pores Calculate the hydraulic radius for capillary condensation in Meso-pores. Hydraulic radius is 2D, width of an infinite slit. RT ln where:

γ vl rk

p γv l = − p◦ rk

≡ ≡ ≡

[email protected]

surface tension liquid molar volume hydraulic radius




BJH Example Data

Nitrogen Isotherm, Amorphous Silica-Alumina Adsorption Desorption

Amorphous Silica Alumina Surface area 214 m2 /g


400 350 300 250 200 150 100 50 0 0

0.2

0.4

0.6

0.8 o

Relative Pressure, p/p

[email protected]


1



BJH Example Data

0.7

BET Surface area - 214 m2 /g

Cumulative Pore Volume, cm3/g

0.6

Amorphous Silica Alumina

0.5 0.4 0.3 0.2 0.1 0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

0.7


0.5 0.4

dV/dD


0.6


0.3 0.2 0.1 0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

300


Cumulative Pore Area, m2/g

250


200

150

100

50

0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

300

200 dSA/dD



250


150

100

50

0 10

[email protected]

100 D, angstroms


1000



BJH Pore Calculations Adsorption Data

0.7

2 1.8

0.6


pore volume, cm3/g

0.5

1.4 1.2

0.4

1 0.3

0.8 0.6

0.2

0.4 0.1 0.2 0

0 10

100 width, Å

[email protected]


dV/d(log(D)), (cm3/g)/Å

1.6




BJH Pore Calculations Desorption Data

0.7

4.5 4

0.6


pore volume, cm3/g

0.5 3 0.4

2.5

0.3

2 1.5

0.2 1 0.1

0.5

0

0 10

100 width, Å

[email protected]



3.5




BJH Example Data

Nitrogen Adsorption, MCM-41

Mesoporous Silica Surface area 926.8 m2 /g


600

Adsorption

500

400

300

200

100

0 0

0.2

0.4

0.6

0.8 o

Relative Pressure, p/p

[email protected]


1



BJH Example Data

1

Amorphous Silica Alumina BET Surface area - 926.8 m2 /g


0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

1

BET Surface area - 926.8 m2 /g

0.8 0.7 0.6 dV/dD



0.9

0.5 0.4 0.3 0.2 0.1 0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

1000 900



800


700 600 500 400 300 200 100 0 10

[email protected]

100 D, angstroms


1000



BJH Example Data

1000 900

700 600 dSA/dD



800


500 400 300 200 100 0 10

[email protected]

100 D, angstroms


1000



Mercury Intrusion Porosimetry

[email protected]




Sample cell - Penetrometer

[email protected]




Low Pressure Analysis

[email protected]




High Pressure Analysis

[email protected]




Sample cell - Penetrometer

[email protected]




Washburn equation Intrusion Force P ·A=P ·

πd 2 4

Resistance Force friction = πdγ cos(θ) Force Balance P·

πd 2 = πdγ cos(θ) 4

Washburn Equation d=

4γ cos(θ) P

[email protected]




“Ink-bottle” Pores Trap Hg in the sample - extrusion rarely follows intrusion

[email protected]




“Ink-bottle” Pores

[email protected]




Effect of equillibrium time

[email protected]




Pore size distributions

[email protected]




Alumina

Total Intrusion Volume Total Pore Area Median Pore Diameter (Volume) Median Pore Diameter (Area) Average Pore Diameter (4V/A) Bulk Density at 0.56 psia Apparent (skeletal) Density Porosity Stem Volume Used

[email protected]

1.2166 305.880 0.0171 0.0084 0.0159 0.6636 3.4454 80.7390 60 %


mL/g m2 /g µm µm µm g/mL g/mL %



Summary Data Total Intrusion Volume - capacitance to volume measurement Total Pore Area - we have used the Washburn equation to calculate a size for each pressure. This diameter is then used with the incremental volume to determine the area of a cylinder. Median Pore Diameter 1

2

by Volume - the diameter is calculated at the pressure corresponding to 50% of the total intrussion volume. by Area - the diameter is calculated at the pressure corresponding to 50% of the total intrussion Area.

Average pore diameter - 4V/A

[email protected]




Density and porosity

Bulk density - actually an envelope density determined by the quantity of Hg in the penetrometer empty (calibrated) versus the quantity at low pressure with the sample. Apparent density - similar to true density - density of the material determined at high pressure and subject to compressibility effects. Porosity - using both the bulk and apparent density to determine percentage of void space = 100*(1 - ρB /ρA )

[email protected]





1.4

Volume

1.2

Intrusion, ml/g

1.0 0.8 DV

0.6 0.4 0.2 0.0 1000

100

10

1 Pore width, µm

[email protected]

0.1

0.01


0.001




350.0

Volume Area

1.2

300.0

1.0

250.0

0.8

200.0 DV

0.6

DA

150.0

0.4

100.0

0.2

50.0

0.0 1000

100

10

1 Pore width, µm

[email protected]

0.1

0.01

0.0 0.001


Pore area, m2/g

Intrusion, ml/g

1.4




350.0

Volume Area

1.2

300.0

1.0

250.0

0.8

4V/A

200.0

DV

0.6

DA

150.0

0.4

100.0

0.2

50.0

0.0 1000

100

10

1 Pore width, µm

[email protected]

0.1

0.01

0.0 0.001


Pore area, m2/g

Intrusion, ml/g

1.4




1.4

2.5

Cumulative Intrusion Log Differential Intrusion

1.2

Intrusion, ml/g

1.5

0.8 0.6

1.0

0.4 0.5 0.2 0.0 1000

100

10

1

0.1

0.01

0.0 0.001

Pore width, µm

[email protected]


Log differential intrusion

2.0 1.0



Porosity of tablets Tableting process influences pore size and ultimately dissolution Use the mercury intrusion to evaluate the porosity of tablets Excedrin Tablet 0.07

Intrusion Extrusion

Intrusion Volume, cm3/g

0.06 0.05 0.04 0.03 0.02 0.01 0 1

10

100 1000 Pressure, psia

[email protected]

10000


100000



Intrusion volume of Excedrin tablet Excedrin Tablet 0.07

Intrusion


0.06 0.05 0.04 0.03 0.02 0.01 0 100

10

[email protected]

1 0.1 Pressure, psia

0.01


0.001



Intrusion and pore size of an Excedrin tablet Excedrin Tablet 0.07

0.045 0.04

0.06

0.03 0.04

0.025

0.03

0.02 0.015

0.02 0.01 0.01

0.005

0 100

10

1 Size, µm

[email protected]

0.1

0.01

0 0.001


Log Differential Intrusion


0.035 0.05



Effect of breaking the Excedrin tablet Excedrin 0.07

0.05

Tablet Broken

0.045

0.06

0.035 0.03

0.04

0.025 0.03

0.02 0.015

0.02

0.01 0.01 0.005 0 100

10

1 Size, µm

[email protected]

0.1

0.01

0 0.001




0.04 0.05



Acetaminophen tablet Acetaminophen Tablet


0.07

0.09

Tablet Broken

0.08 0.07

0.06

0.06

0.05

0.05 0.04 0.04 0.03

0.03

0.02

0.02

0.01

0.01

0 100

10

1

0.1

0.01

Size, µm

[email protected]


0 0.001


0.08



Acetaminophen caplet Acetaminophen Caplet 0.14

0.2

Caplet Broken

0.18

0.12

0.14 0.12

0.08

0.1 0.06

0.08 0.06

0.04

0.04 0.02 0.02 0 100

10

1

0.1

0.01

Size, µm

[email protected]


0 0.001



0.16 0.1



Tablets and Caplets Excedrin, Acetaminophen Tablets and Caplets 0.14


0.12

Excedrin Acetaminophen Tab Acetaminophen Cap

0.1 0.08 0.06 0.04 0.02 0 100

10

[email protected]

1 Size, µm

0.1

0.01


0.001



Tablets and Caplets Excedrin, Acetaminophen Tablets and Caplets 0.2

Log Differential Intrusion, cm3/g

0.18

Excedrin Acetaminophen Tab Acetaminophen Cap

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 100

10

[email protected]

1 Size, µm

0.1

0.01


0.001


Structures

Common Structures 1 ZSM-5 Nan [Aln Si96−n O192 ], n > 27 MFI - Structure Code 2

13x (Na2 , Ca, Mg )29 [Al58 Si134 O184 ] FAU - Structure Code

3

H-Y H53.3 [Al53.3 Si138.7 O357.3 ] FAU - Structure Code

[email protected]



Structures

Common Structures 1 ZSM-5 Nan [Aln Si96−n O192 ], n > 27 MFI - Structure Code 2

13x (Na2 , Ca, Mg )29 [Al58 Si134 O184 ] FAU - Structure Code

3

H-Y H53.3 [Al53.3 Si138.7 O357.3 ] FAU - Structure Code

[email protected]



Adsortives Nitrogen Argon

[email protected]



N2 Adsorption on Faujasite, 13X 160

FAU Structures 13x H-Y


140

Cation Na+

120 100 80 60 40 20 0 1e-008

1e-007

1e-006

1e-005 p/po

[email protected]


0.0001

0.001

0.01


N2 Adsorption on Faujasite, H-Y 250

Cation H+



200

150

100

50

0 1e-007

1e-006

1e-005

0.0001

0.001

p/po

[email protected]


0.01

0.1

1


N2 Adsorption on Faujasite 250

Cation H+ Na+



200

150

100

50

0 1e-008

1e-007

1e-006

1e-005

0.0001 p/po

[email protected]


0.001

0.01

0.1

1


Ar Adsorption on ZSM-5 200 180 160

SiO2:Al2O3 30:1 55:1 80:1 280:1

MFI Structure SiO2 :Al2 O3 ratios 30, 55, 80, and 280

140 120 100

Argon isotherms collected at 77 K

80 60

Significant transition

40 20 0 1e-007

1e-006

1e-005

0.0001

0.001

0.01

[email protected]

0.1

1



Ar Adsorption on ZSM-5 250

200

SiO2:Al2O3 30:1 55:1 80:1 280:1

MFI Structure SiO2 :Al2 O3 ratios 30, 55, 80, and 280

150

Argon isotherms collected at 77 K

100

Significant transition

50

0 1e-007

1e-006

1e-005

0.0001

0.001

0.01

[email protected]

0.1

1



Microporosity - Dubinin Common Models Dubinin Horwath and Kawazoe Density Functional Theory Generalized Form po A = RT ln p A n W = W0 exp − βE0

[email protected]



Microporosity - HK Slit Pores Common Models Dubinin Horwath and Kawazoe Density Functional Theory Slit-shape Pore Geometry

(Na Aa + NA AA ) RT ln = K × σ 4 (l − d) σ4 σ 10 σ4 σ 10 − − + 3 (l − d/2)3 9 (l − d/2)9 4 (d/2)4 9 (d/2)9 p po

[email protected]



Microporosity - HK Cylindrical Pores Common Models Dubinin Horwath and Kawazoe Density Functional Theory Cylindrical-shape Pore Geometry

(Na Aa + NA AA ) p 3 RT ln = πK × po 4 d4 " 10 4 !# inf X d 2k 21 d d 1 1− − αk − βk 2k + 1 rp 32 rp rp k=0

[email protected]



Microporosity - DFT

Common Models Dubinin Horwath and Kawazoe Density Functional Theory Integral Equation of Adsorption Z Q(p) = dH q(p, h) f (H)

[email protected]



ZSM-5 Pore Size Distribution 200 180

SiO2:Al2O3 30:1

H-K Model Saito-Foley Model Cylindrical Pore Geometry Nitrogen, 77 K


160 140 120 100 80 60 40 20 0 1e-008

1e-007

1e-006

1e-005

0.0001 p/po

[email protected]


0.001

0.01

0.1

1


ZSM-5 Pore Size Distribution

0.2

SiO2:Al2O3 30:1

0.18 0.16

Cylindrical Pore Geometry Nitrogen, 77 K

0.14 dV/dW, cm3/g-A

H-K Model Saito-Foley Model

0.12 0.1 0.08 0.06 0.04 0.02 0 4

5

6

7

8

9 W, A

[email protected]


10

11

12

13



0.5

SiO2:Al2O3 30:1 55:1 80:1 280:1

0.45 0.4

Cylindrical Pore Geometry Nitrogen, 77 K

dV/dW, cm3/g-A


0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 4

5

6

7

8

9 W, A

[email protected]


10

11

12

13



160

SiO2:Al2O3 280:1

H-K Model Saito-Foley Model Cylindrical Pore Geometry Argon, 87 K


140 120 100 80 60 40 20 0 1e-007

1e-006

1e-005

0.0001 p/po

[email protected]


0.001

0.01

0.1

1



0.07

SiO2:Al2O3 280:1

0.06

Cylindrical Pore Geometry Argon, 87 K

0.05 dV/dW, cm3/g-A


0.04 0.03 0.02 0.01 0 4

[email protected]

5

6

7

8

9 10 W, A


11

12

13

14

15



0.08

SiO2:Al2O3 280:1 55:1 80:1

0.07

Cylindrical Pore Geometry

0.06 dV/dW, cm3/g-A


0.05 0.04 0.03 0.02

Argon, 87 K

0.01 0 4

[email protected]

6

8

10 W, A


12

14

16


DFT Pore Size Distribution 0.35

SiO2:Al2O3 ZSM-5 30:1

0.3

DFT Model Tarazona Model

3

dV/dW, cm /g-A

0.25 0.2


0.15 0.1

Nitrogen, 77 K ZSM-5

0.05 0 1

10

100

1000

W, A

[email protected]




SiO2:Al2O3 ZSM-5 30:1 H-Y 5:1

0.3

DFT Model Tarazona Model

3

dV/dW, cm /g-A

0.25 0.2


0.15

Nitrogen, 77 K

0.1

ZSM-5 0.05

H-Y 0 1

10

100

1000

W, A

[email protected]




20

0.8

18

12 0.5 10 0.4 8 0.3

6

0.2

3

pore volume, cm3/g

14

0.6

dV/d(log(D)), (cm /g)/Å

16

0.7

DFT Model Cylindrical Pores Oxide Model

4

0.1

2

0

0 10

100 width, Å

[email protected]


Cylindrical Pore Geometry Nitrogen, 77 K MCM-41


X Zeolite 0.25

7 6

pore volume, cm3/g

5 0.15

4 3

0.1

2 0.05 1 0 1

10 width, Å

[email protected]


0 100


0.2


Y Zeolite 0.3

2.5

2

0.2 1.5 0.15 1 0.1 0.5

0.05

0 1

10 width, Å

[email protected]


0 100


pore volume, cm3/g

0.25


Summary Chemistry effects Composition influnces the adsorption potential - for example the alkaline zeolites adsorbed nitrogen at very low pressure. Structure Adsorption potential also follows pore size - for example a 5˚ A pore adsorbs nitrogen at lower pressures than an 8˚ A pore. Surface Area Surface area increases as pore size decreases

[email protected]



Summary cont’d Preparation The preparation temperature strongly influences surface area. As prep temperature was increased for oxides the SSA increased; while the opposite was observed for stearates - increasing prep temperature reduced the surface area. Porosity Mesoporosity is a function of pressure and not as strongly dependent upon chemistry like the micro porous materials. Porosity of Excipients Common excipients do not exhibit significant levels of porosity as we observed with silica. [email protected]



Summary cont’d

Macro porosity Mercury porosimetry allows us to understand the larger pores in a material Tablets The pore size of consumer tablets is very consistent and breaking a tablet does not provide additional access to the API. This should provide a consistent release of the API.

[email protected]


CHARACTERIZATION OF POWDERS AND POROUS MATERIALS

Recommend Documents